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Astron. Astrophys. 325, 401-413 (1997)

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5. Bremsstrahlung

Electron-positron bremsstrahlung is a well-known QED process, but the calculation of its fully differential cross section for the photon production is very laborious, the resulting cross section formula is extremely lengthy and it was obtained quite recently (Haug 1985a, b). In [FORMULA] -collisions both particles radiate, and that brings some uncertainties in calculation of the particle energy loss, increasing particularly as the positron energy closes in the electron gas temperature. The exact energy loss rate can be obtained using the cross section differential in the energy of the outgoing positrons, but no expression for this quantity is available. As it will be shown, the bremsstrahlung energy loss is small in comparison with Coulomb and Compton scattering losses, and that allows us to approximate it by the radiated energy rate. We shall, hereafter, speak about the particle energy loss taking into account the above remark.

An average energy loss through bremsstrahlung is given by

[EQUATION]

where [FORMULA] is the bremsstrahlung differential cross section in the CMS, and k is the LS energy of the radiated photon. It can be expressed as

[EQUATION]

where [FORMULA]. For [FORMULA] bremsstrahlung Haug (1985c) gives an approximation

[EQUATION]

where [FORMULA] is the fine structure constant, and [FORMULA], [FORMULA] are the CMS variables given by Eq. (19). The same for [FORMULA] bremsstrahlung is (Haug 1975)

[EQUATION]

Then, starting from Eq. (14) and taking into account Eq. (29) we get

[EQUATION]

[EQUATION]

[EQUATION]

[EQUATION]

In a hydrogen plasma the moving positron suffers energy losses due to [FORMULA] - and ep -bremsstrahlung. For equal [FORMULA] and p densities, [FORMULA] bremsstrahlung gives the dominant contribution to the energy loss in the whole energy range. At the high energy limit [FORMULA] -bremsstrahlung energy loss becomes equal to that of ep and exactly twice the ee energy loss; herewith in the Born approximation [FORMULA] and [FORMULA] cases are identical (Jauch & Rohrlich, 1976). An expression for energy loss due to ep -bremsstrahlung was obtained by Stickforth (1961)

[EQUATION]

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© European Southern Observatory (ESO) 1997

Online publication: May 5, 1998

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